Rear ended, no visible damage, should I report to insurance?

I was at a red light and a car rear ended me hard enough to push my car forward a bit. She was very nice, admitted fault (said she was zipping her rain jacket and not looking), and provided me with all her info. We pulled into a gas station where cops already were dealing with something else, and the cop we talked to said if there’s no visible damage/it’s less than $1,000, we don’t need to file a police report, so we didn’t.

I’ve read on here a number of things that confuse me, so have a few questions:

-even if there isn’t any visible damage to the bumper, I have read that there could be damage underneath. Should I get it inspected and then file a claim or call insurance and have them involved all along?

-I’m in NC and worried that my insurance points will go up even though I’m not at fault. Is this true that this happens sometimes? I have Cincinnati Insurance.

-my gut is to not file a claim as I truly don’t think my car has damage and I don’t want to deal with the hassle, but I’m also worried that this person could go and file a bogus claim against me, so is it possible to tell insurance what happened so it’s on the record even if my car doesn’t need any repairs? Her car also looked fine and didn’t seem to have any scrapes or dents.

Thanks in advance for your guidance!